Along with his compositional activities, he received a Ph.D. on the gap between perceptive and analytical complexity in music at EHESS and CNRS, and has written numerous theoretical articles and a book. He worked at IRCAM, first in 1998 as artistic director of the Studio Online Project, and then as pedagogical advisor for the organisation of colloquium and cultural events (1999-2000). He also lectured in computer music at the musicology dept. of the Sorbonne University (Paris), and from 2004-2006 taught orchestration for graduate composition students at the Hochschule für Musik Hanns-Eisler in Berlin. He was 2006-2012 Assistant Professor of Composition at Columbia University in New York. He was appointed from 2012 to 2017 senior professor for composition at the Hochschule für Musik Detmold in Germany, and has been senior professor for composition at the Hochschule für Musik und Theater “Felix Mendelssohn-Bartholdy” in Leipzig since October 2017.

As a composer, he is laureate of the Singer-Polignac Foundation (1995) and the DAAD Berliner Künstlerprogramm (one year residency in 2001 in Berlin). His orchestral work Hérédo-Ribotes was nominated at the International Rostrum of composers of Unesco (2002). He received the French Prix de Rome (residency in 2002-2003 in the Villa Medicis / French academy in Rome). He won the 2004 Förderpreis from the Ernst von Siemens Foundation for Music.

His works for soloists, chamber music, ensemble, orchestra and computer, have been performed across in the world by ensembles and soloists including C. Delangle, l’Itinéraire, the Ensemble Recherche, 2E2M, the Argento Ensemble, the Ensemble Modern, the neue Vocalsolisten Stuttgart, the Tokyo Philharmonic Orchestra, the Orchestre National de France and the Berlin Radio Symphony Orchestra, among others. His works currently focus on the relation between the whole and the detail, paradoxes of perception and musical grammatology, and techniques of cross-rhythms generalized to every musical parameter. Lévy's music is published by Billaudot (until 2008), Ricordi (2008-2018) and, since 2018, Edition Peters.